Pulse instabilities in harmonic active mode-locking: a time-delayed approach.

We propose a time-delayed model for the study of active mode-locking that is valid for large values of the round trip gain and losses. It allows us to access the typical regimes encountered in semiconductor lasers and to perform an extended bifurcation analysis. Close to the harmonic resonances and to the lasing threshold, we recover the Hermite-Gauss solutions.

Square waves and Bykov T-points in a delay algebraic model for the Kerr-Gires-Tournois interferometer.

We study theoretically the mechanisms of square wave formation of a vertically emitting micro-cavity operated in the Gires-Tournois regime that contains a Kerr medium and that is subjected to strong time-delayed optical feedback and detuned optical injection. We show that in the limit of large delay, square wave solutions of the time-delayed system can be treated as relative homoclinic solutions of an equation with an advanced argument. Based on this, we use concepts of classical homoclinic bifurcation theory to study different types of square wave solutions.

Temporal localized states and square-waves in semiconductor micro-resonators with strong time-delayed feedback.

In this paper, we study the dynamics of a vertically emitting micro-cavity operated in the Gires-Tournois regime that contains a semiconductor quantum-well and that is subjected to strong time-delayed optical feedback and detuned optical injection. Using a first principle time-delay model for the optical response, we disclose sets of multistable dark and bright temporal localized states coexisting on their respective bistable homogeneous backgrounds. In the case of anti-resonant optical feedback, we identify square-waves with a period of twice the round-trip in the external cavity.

Artificial optoelectronic spiking neuron based on a resonant tunnelling diode coupled to a vertical cavity surface emitting laser.

Excitable optoelectronic devices represent one of the key building blocks for implementation of artificial spiking neurons in neuromorphic (brain-inspired) photonic systems. This work introduces and experimentally investigates an opto-electro-optical (O/E/O) artificial neuron built with a resonant tunnelling diode (RTD) coupled to a photodetector as a receiver and a vertical cavity surface emitting laser as a transmitter. We demonstrate a well-defined excitability threshold, above which the neuron produces optical spiking responses with characteristic neural-like refractory period.

Square-wave generation in vertical external-cavity Kerr-Gires-Tournois interferometers.

We study theoretically the mechanisms of square-wave (SW) formation in vertical external-cavity Kerr-Gires-Tournois interferometers in the presence of anti-resonant injection. We provide simple analytical approximations for their plateau intensities and for the conditions of their emergence. We demonstrate that SWs may appear via a homoclinic snaking scenario, leading to the formation of complex-shaped multistable SW solutions.

A normal form for frequency combs and localized states in Kerr-Gires-Tournois interferometers.

We elucidate the mechanisms that underlay the formation of temporal localized states and frequency combs in vertical external-cavity Kerr-Gires-Tournois interferometers. We reduce our first-principles model based upon delay algebraic equations to a minimal pattern formation scenario. It consists in a real cubic Ginzburg-Landau equation modified by high-order effects such as third-order dispersion and nonlinear drift, which are responsible for generating localized states via the locking of domain walls connecting the high and low intensity levels of the injected micro-cavity.

Influence of time-delayed feedback on the dynamics of temporal localized structures in passively mode-locked semiconductor lasers.

In this paper, we analyze the effect of optical feedback on the dynamics of a passively mode-locked ring laser operating in the regime of temporal localized structures. This laser system is modeled by a set of delay differential equations, which include delay terms associated with the laser cavity and the feedback loop. Using a combination of direct numerical simulations and path-continuation techniques, we show that the feedback loop creates echoes of the main pulse whose position and size strongly depend on the feedback parameters.

Conservative Solitons and Reversibility in Time Delayed Systems.

Time delayed dynamical systems have proven to be a fertile framework for the study of physical phenomena. In natural sciences, their uses have been limited to the study of dissipative dynamics. In this Letter, we demonstrate the existence of nonlinear reversible conservative time delayed systems.

Simplified description of dynamics in neuromorphic resonant tunneling diodes.

In this article, the standard theoretical model accounting for a double barrier quantum well resonant tunneling diode (RTD) connected to a direct current source of voltage is simplified by representing its current-voltage characteristic with an analytically approachable, anti-symmetric N-shaped function. The time and variables involved are also transformed to reduce the number of parameters in the model. Responses observed in previous, more physically accurate studies are reproduced, including slow-fast dynamics, excitability, and bistability, relevant for spiking signal processing.

Wiggling instabilities of temporal localized states in passively mode-locked vertical external-cavity surface-emitting lasers.

We analyze the emergence of wiggling temporal localized states in a passively mode-locked vertical external-cavity surface-emitting laser composed by a gain chip and a resonant saturable absorber mirror. We show that the wiggling instability stems from the interplay between the third-order dispersion induced by the micro-cavities and their frequency mismatch. The latter is identified as an experimentally crucial parameter defining the range of existence of stable emission.

Manipulation of temporal localized structures in a vertical external-cavity surface-emitting laser with optical feedback.

We analyze the effect of optical feedback on the dynamics of an external-cavity passively mode-locked surface-emitting laser operating in the regime of temporal localized structures. Depending on the ratio between the cavity round trip time and the feedback delay, we show experimentally that feedback acts as a solution selector that either reinforces or hinders the appearance of one of the multistable harmonic arrangements of pulses. Our theoretical analysis reproduces well the experiment and allows us to evidence asymmetrical resonance tongues due to the parity symmetry-breaking induced by gain depletion.

How carrier memory enters the Haus master equation of mode-locking.

We present a generalization of the Haus master equation in which a dynamical boundary condition allows to describe complex pulse trains, such as the -switched and harmonic transitions of passive mode-locking, as well as the weak interactions between localized states. As an example, we investigate the role of group velocity dispersion on the stability boundaries of the -switched regime and compare our results with that of a time-delayed system.

Hopping and emergent dynamics of optical localized states in a trapping potential.

The position and motion of localized states of light in propagative geometries can be controlled via an adequate parameter modulation. Here, we show theoretically and experimentally that this process can be accurately described as the phase locking of oscillators to an external forcing and that non-reciprocal interactions between light bits can drastically modify this picture. Interactions lead to the convective motion of defects and to an unlocking as a collective emerging phenomenon.

Bound states of light bullets in passively mode-locked semiconductor lasers.

In this paper, we analyze the dynamics and formation mechanisms of bound states (BSs) of light bullets in the output of a laser coupled to a distant saturable absorber. First, we approximate the full three-dimensional set of Haus master equations by a reduced equation governing the dynamics of the transverse profile. This effective theory allows us to perform a detailed multiparameter bifurcation study and to identify the different mechanisms of instability of BSs.

Topological localized states in the time delayed Adler model: Bifurcation analysis and interaction law.

The time-delayed Adler equation is the simplest model for an injected semiconductor laser with coherent injection and optical feedback. It is, however, able to reproduce the existence of topological localized structures (LSs) and their rich interactions. In this paper, we perform the first extended bifurcation analysis of this model and we explore the mechanisms by which LSs emerge.

Discrete light bullets in passively mode-locked semiconductor lasers.

In this paper, we analyze the formation and dynamical properties of discrete light bullets in an array of passively mode-locked lasers coupled via evanescent fields in a ring geometry. Using a generic model based upon a system of nearest-neighbor coupled Haus master equations, we show numerically the existence of discrete light bullets for different coupling strengths. In order to reduce the complexity of the analysis, we approximate the full problem by a reduced set of discrete equations governing the dynamics of the transverse profile of the discrete light bullets.

Mesoscopic Limit Cycles in Coupled Nanolasers.

Two coupled nanolasers exhibit a mode switching transition, theoretically described by mode beating limit cycle oscillations. Their decay rate is vanishingly small in the thermodynamic limit, i.e.

Tunable Kerr frequency combs and temporal localized states in time-delayed Gires-Tournois interferometers.

In this Letter, we study theoretically a new setup allowing for the generation of temporal localized states (TLSs) and frequency combs. The setup is compact (a few centimeters) and can be implemented using established technologies, while offering tunable repetition rates and potentially high power operation. It consists of a vertically emitting micro-cavity, operated in the Gires-Tournois regime, containing a Kerr medium strong time-delayed optical feedback, and detuned optical injection.

Third Order Dispersion in Time-Delayed Systems.

Time-delayed dynamical systems materialize in situations where distant, pointwise, nonlinear nodes exchange information that propagates at a finite speed. However, they are considered devoid of dispersive effects, which are known to play a leading role in pattern formation and wave dynamics. We show how dispersion may appear naturally in delayed systems and we exemplify our result by studying theoretically and experimentally the influence of third order dispersion in a system composed of coupled optical microcavities.

Temporal localized structures in mode-locked vertical external-cavity surface-emitting lasers.

Temporal localized states (TLSs) are individually addressable structures traveling in optical resonators. They can be used to obtain bits of information and generate frequency combs with tunable spectral density. We show that a pair of specially designed nonlinear mirrors, a 1/2 vertical-cavity surface-emitting laser and a semiconductor saturable absorber, coupled in self-imaging conditions, can lead to the generation of such TLSs.

Light bullets in a time-delay model of a wide-aperture mode-locked semiconductor laser.

Recently, a mechanism of formation of light bullets (LBs) in wide-aperture passively mode-locked lasers was proposed. The conditions for existence and stability of these bullets, found in the long cavity limit, were studied theoretically under the mean field (MF) approximation using a Haus-type model equation. In this paper, we relax the MF approximation and study LB formation in a model of a wide-aperture three section laser with a long diffractive section and short absorber and gain sections.

Functional mapping for passively mode-locked semiconductor lasers.

We present a modern approach for the analysis of passively mode-locked semiconductor lasers that allows for efficient parameter sweeps and time jitter analysis. It permits accessing the ultralow repetition rate regime where pulses become localized states. The analysis including slow (e.

Interactions and collisions of topological solitons in a semiconductor laser with optical injection and feedback.

We present experimental and numerical results about dynamical interactions of topological solitons in a semiconductor laser with coherent injection and feedback. We show different kind of interactions such as repulsion, annihilation, or formation of soliton bound states, depending on laser parameters. Collisions between single structures and bound states conserve momentum and charge.